加权中间里奇曲率下界下的Fenchel-Willmore-Chen不等式
Fenchel-Willmore-Chen inequality under lower bounds on weighted intermediate Ricci curvature
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中文总结 AI 辅助
针对具1-Bakry-Émery k-里奇曲率下界的光滑度量测度空间，建立Fenchel-Willmore-Chen不等式并给出统一证明，同时证明非负1-加权里奇曲率的Sobolev与等周不等式。
中文摘要 AI 辅助
我们针对具有1-Bakry-Émery k-里奇曲率下界的光滑度量测度空间，建立了Fenchel-Willmore-Chen不等式，该结果推广了此前的结论并给出了统一证明；此外，还证明了非负1-加权里奇曲率的Sobolev不等式与等周不等式。
英文摘要
We establish a Fenchel-Willmore-Chen inequality for smooth metric measure spaces with a lower bound on the 1-Bakry-Emery k-Ricci curvature. This extends previous results and yields a unified proof. In addition, a Sobolev and isoperimetric inequality for nonnegative 1-weighted Ricci curvature is proven.
